Meredith Corp., the owner of Better Homes & Gardens and Allrecipes, has struck a deal to buy magazine publisher Time Inc. for $1.85 billion in cash, a significant bet on the future of the magazine industry as media companies try to find their footing in an increasingly digital world.

Meredith, based in Des Moines, Iowa, has agreed to pay $18.50 a share for Time, the fabled New York publisher of Fortune, People and Sports Illustrated, the companies said. The boards of both companies have approved the transaction.